The development of non-invasive systems and methods for the transcutaneous measurement of blood analytes, such as glucose, remain important for the diagnosis and treatment of a variety of conditions. Conventional blood sampling methods are painful and have other undesirable features. However, none of the non-invasive methods being developed has demonstrated sufficient accuracy or reproducibility for clinical use. A major obstacle in achieving reproducible optical measurement such as Raman spectroscopy is the variation in optical properties (absorption and scattering) from measurement site to site, from subject to subject, and over time. Optical properties are important because the amount of absorption and scattering in a sample greatly influences the volume of tissue sampled by the excitation light and the magnitude of the collected Raman signal. A method to correct for this is necessary for the success because of the way calibration is performed. Reference concentrations obtained from a blood glucose or interstitial glucose measurement are used to correlate a given Raman spectrum with the concentration of glucose that spectrum should contain. Significant errors in calibration transfer are prone to occur if the number of glucose molecules sampled by the Raman instrument on day two is different than day one and yet the concentration of glucose molecules in the blood is the same. In other words, spectroscopic techniques such as Raman are sensitive to the number of glucose molecules sampled in the blood-tissue matrix, whereas the reference measurement provides the concentration (number÷volume) of glucose molecules in the blood or interstitial fluid.
To further improve optical measurements of blood analytes multivariate calibration has been used as an analytical technique for extracting analyte concentrations in complex chemical systems that exhibit linear response. Multivariate techniques are particularly well suited to analysis of spectral data, since information about all the analytes can be collected simultaneously at many wavelengths. Explicit calibration methods are often used when all of the constituent spectra can be individually measured or pre-calculated. Examples are ordinary least squares (OLS) and classical least squares (CLS). When individual spectra are not all known, implicit modeling techniques are often adapted. Principle component regression (PCR) and partial least squares (PLS) are two frequently used methods in this category. In either case, the goal of multivariate calibration is to obtain a spectrum of regression coefficients, b, such that an analyte's concentration, c, can be accurately predicted by taking the scalar product of b with a spectrum, s:c═ST·b  (1)(Lowercase boldface type denotes a column vector, uppercase boldface type a matrix; and the superscript T denotes transpose.) The regression vector, b, is unique in an ideal noise-free linear system without constituent correlations, and the goal of both implicit and explicit schemes is to find an accurate approximation to b for the system of interest.
Explicit and implicit methods have their own advantages and limitations. Explicit methods provide transparent models with easily interpretable results. However, they require high quality spectra and accurate concentration measurements of each of the constituent analytes (or equivalent information), which may be difficult to obtain, particularly in in vivo applications. Implicit methods require only high quality calibration spectra and accurate concentration measurements of the analyte of interest, (the “calibration data”), greatly facilitating system design. However, unlike explicit methods, the performance of implicit methods can both be simply judged by conventional statistical measures such as goodness of fit. Spurious effects such as system drift and co-variations among constituents can be incorrectly interpreted as legitimate correlations. Furthermore, implicit methods such as PCR and PLS lack the ability to incorporate information about the system or analytes, in addition to the calibration data, into b. Such prior information can, in principle, improve measurement accuracy. In particular, in many cases it is desirable to use prior spectral information about the constituent analytes. Such information generally helps stabilize and enhance deconvolution, classification and/or inversion algorithms. In multivariate calibration, methods combining explicit and implicit modeling, such as hybrid linear analysis (HLA), achieve the same goal by removing the contribution of the known analyte spectrum of interest from the sample spectra. Thus, there remains a need for further improvements in systems and methods for the non-invasive measurement of blood analytes.